We are given that according to a survey, the average American person watches TV for 3 hours per week. She surveys 19 New Yorkers randomly and asks them about their amount of TV each week, on average. From the data, the sample mean time is 2.5 hours per week, and the sample standard deviation (s) is 0.9 hours.

We have to test if the amount of TV in New York City is less than the national average.

Let Null Hypothesis, $H_0$ : $\mu$ $\leq$ 3 {means that the amount of TV in New York City is less than the national average}

Alternate Hypothesis, $H_1$ : $\mu$ > 3 {means that the amount of TV in New York City is more than the national average}

The test statistics that will be used here is One-sample t-test statistics;

T.S. = $\frac{\bar X - \mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean time = 2.5 hours per week

$s$ = sample standard deviation = 0.09 hours

n = sample size = 19

So, <u>test statistics</u> = $\frac{2.5 - 3}{\frac{0.9}{\sqrt{19} } }$ ~ $t_1_8$

= -2.422

Therefore, the test statistic (t-value) of this one-mean hypothesis test (with σ unknown) is -2.422.

8 0

4 years ago

A pair of tangents to a circle which is inclined to each other at an angle of 60 degree are drawn at ends of two radii. The angl

Sever21 [200]

Answer:

The angle between these radii must be 120º.

Step-by-step explanation:

According to Euclidean Geometry, two tangents to a circle are symmetrical to each other and the axis of symmetry passes through the center of the circle and, hence, each tangent is perpendicular to a respective radius. We represent the statement in the diagram included below.

Then, we calculate the angle of the radius with respect to the axis of symmetry by knowing the fact that sum of internal angles within triangle equals 180º. That is to say:

$\theta = 180^{\circ}-90^{\circ}-30^{\circ}$

$\theta = 60^{\circ}$

And the angle between these two radii is twice the result.

$\theta' = 2\cdot \theta$

$\theta' = 120^{\circ}$

The angle between these radii must be 120º.

5 0

3 years ago